signature hashmap_FunsTheory = sig type thm = Thm.thm (* Definitions *) val core_num_u32_max_body_def : thm val core_num_u32_max_c_def : thm val hash_key_fwd_def : thm val hash_map_allocate_slots_fwd_def : thm val hash_map_allocate_slots_loop_fwd_def : thm val hash_map_clear_fwd_back_def : thm val hash_map_clear_loop_fwd_back_def : thm val hash_map_contains_key_fwd_def : thm val hash_map_contains_key_in_list_fwd_def : thm val hash_map_contains_key_in_list_loop_fwd_def : thm val hash_map_get_fwd_def : thm val hash_map_get_in_list_fwd_def : thm val hash_map_get_in_list_loop_fwd_def : thm val hash_map_get_mut_back_def : thm val hash_map_get_mut_fwd_def : thm val hash_map_get_mut_in_list_back_def : thm val hash_map_get_mut_in_list_fwd_def : thm val hash_map_get_mut_in_list_loop_back_def : thm val hash_map_get_mut_in_list_loop_fwd_def : thm val hash_map_insert_fwd_back_def : thm val hash_map_insert_in_list_back_def : thm val hash_map_insert_in_list_fwd_def : thm val hash_map_insert_in_list_loop_back_def : thm val hash_map_insert_in_list_loop_fwd_def : thm val hash_map_insert_no_resize_fwd_back_def : thm val hash_map_len_fwd_def : thm val hash_map_move_elements_from_list_fwd_back_def : thm val hash_map_move_elements_from_list_loop_fwd_back_def : thm val hash_map_move_elements_fwd_back_def : thm val hash_map_move_elements_loop_fwd_back_def : thm val hash_map_new_fwd_def : thm val hash_map_new_with_capacity_fwd_def : thm val hash_map_remove_back_def : thm val hash_map_remove_from_list_back_def : thm val hash_map_remove_from_list_fwd_def : thm val hash_map_remove_from_list_loop_back_def : thm val hash_map_remove_from_list_loop_fwd_def : thm val hash_map_remove_fwd_def : thm val hash_map_try_resize_fwd_back_def : thm val test1_fwd_def : thm val hashmap_Funs_grammars : type_grammar.grammar * term_grammar.grammar (* [hashmap_Types] Parent theory of "hashmap_Funs" [core_num_u32_max_body_def] Definition ⊢ core_num_u32_max_body = Return (int_to_u32 4294967295) [core_num_u32_max_c_def] Definition ⊢ core_num_u32_max_c = get_return_value core_num_u32_max_body [hash_key_fwd_def] Definition ⊢ ∀k. hash_key_fwd k = Return k [hash_map_allocate_slots_fwd_def] Definition ⊢ ∀slots n. hash_map_allocate_slots_fwd slots n = hash_map_allocate_slots_loop_fwd slots n [hash_map_allocate_slots_loop_fwd_def] Definition ⊢ ∀slots n. hash_map_allocate_slots_loop_fwd slots n = if usize_gt n (int_to_usize 0) then do slots0 <- vec_push_back slots ListNil; n0 <- usize_sub n (int_to_usize 1); hash_map_allocate_slots_loop_fwd slots0 n0 od else Return slots [hash_map_clear_fwd_back_def] Definition ⊢ ∀self. hash_map_clear_fwd_back self = do v <- hash_map_clear_loop_fwd_back self.hash_map_slots (int_to_usize 0); Return (self with <|hash_map_num_entries := int_to_usize 0; hash_map_slots := v|>) od [hash_map_clear_loop_fwd_back_def] Definition ⊢ ∀slots i. hash_map_clear_loop_fwd_back slots i = (let i0 = vec_len slots in if usize_lt i i0 then do i1 <- usize_add i (int_to_usize 1); slots0 <- vec_index_mut_back slots i ListNil; hash_map_clear_loop_fwd_back slots0 i1 od else Return slots) [hash_map_contains_key_fwd_def] Definition ⊢ ∀self key. hash_map_contains_key_fwd self key = do hash <- hash_key_fwd key; i <<- vec_len self.hash_map_slots; hash_mod <- usize_rem hash i; l <- vec_index_fwd self.hash_map_slots hash_mod; hash_map_contains_key_in_list_fwd key l od [hash_map_contains_key_in_list_fwd_def] Definition ⊢ ∀key ls. hash_map_contains_key_in_list_fwd key ls = hash_map_contains_key_in_list_loop_fwd key ls [hash_map_contains_key_in_list_loop_fwd_def] Definition ⊢ ∀key ls. hash_map_contains_key_in_list_loop_fwd key ls = case ls of ListCons ckey t tl => if ckey = key then Return T else hash_map_contains_key_in_list_loop_fwd key tl | ListNil => Return F [hash_map_get_fwd_def] Definition ⊢ ∀self key. hash_map_get_fwd self key = do hash <- hash_key_fwd key; i <<- vec_len self.hash_map_slots; hash_mod <- usize_rem hash i; l <- vec_index_fwd self.hash_map_slots hash_mod; hash_map_get_in_list_fwd key l od [hash_map_get_in_list_fwd_def] Definition ⊢ ∀key ls. hash_map_get_in_list_fwd key ls = hash_map_get_in_list_loop_fwd key ls [hash_map_get_in_list_loop_fwd_def] Definition ⊢ ∀key ls. hash_map_get_in_list_loop_fwd key ls = case ls of ListCons ckey cvalue tl => if ckey = key then Return cvalue else hash_map_get_in_list_loop_fwd key tl | ListNil => Fail Failure [hash_map_get_mut_back_def] Definition ⊢ ∀self key ret. hash_map_get_mut_back self key ret = do hash <- hash_key_fwd key; i <<- vec_len self.hash_map_slots; hash_mod <- usize_rem hash i; l <- vec_index_mut_fwd self.hash_map_slots hash_mod; l0 <- hash_map_get_mut_in_list_back l key ret; v <- vec_index_mut_back self.hash_map_slots hash_mod l0; Return (self with hash_map_slots := v) od [hash_map_get_mut_fwd_def] Definition ⊢ ∀self key. hash_map_get_mut_fwd self key = do hash <- hash_key_fwd key; i <<- vec_len self.hash_map_slots; hash_mod <- usize_rem hash i; l <- vec_index_mut_fwd self.hash_map_slots hash_mod; hash_map_get_mut_in_list_fwd l key od [hash_map_get_mut_in_list_back_def] Definition ⊢ ∀ls key ret. hash_map_get_mut_in_list_back ls key ret = hash_map_get_mut_in_list_loop_back ls key ret [hash_map_get_mut_in_list_fwd_def] Definition ⊢ ∀ls key. hash_map_get_mut_in_list_fwd ls key = hash_map_get_mut_in_list_loop_fwd ls key [hash_map_get_mut_in_list_loop_back_def] Definition ⊢ ∀ls key ret. hash_map_get_mut_in_list_loop_back ls key ret = case ls of ListCons ckey cvalue tl => if ckey = key then Return (ListCons ckey ret tl) else do tl0 <- hash_map_get_mut_in_list_loop_back tl key ret; Return (ListCons ckey cvalue tl0) od | ListNil => Fail Failure [hash_map_get_mut_in_list_loop_fwd_def] Definition ⊢ ∀ls key. hash_map_get_mut_in_list_loop_fwd ls key = case ls of ListCons ckey cvalue tl => if ckey = key then Return cvalue else hash_map_get_mut_in_list_loop_fwd tl key | ListNil => Fail Failure [hash_map_insert_fwd_back_def] Definition ⊢ ∀self key value. hash_map_insert_fwd_back self key value = do self0 <- hash_map_insert_no_resize_fwd_back self key value; i <- hash_map_len_fwd self0; if usize_gt i self0.hash_map_max_load then hash_map_try_resize_fwd_back self0 else Return self0 od [hash_map_insert_in_list_back_def] Definition ⊢ ∀key value ls. hash_map_insert_in_list_back key value ls = hash_map_insert_in_list_loop_back key value ls [hash_map_insert_in_list_fwd_def] Definition ⊢ ∀key value ls. hash_map_insert_in_list_fwd key value ls = hash_map_insert_in_list_loop_fwd key value ls [hash_map_insert_in_list_loop_back_def] Definition ⊢ ∀key value ls. hash_map_insert_in_list_loop_back key value ls = case ls of ListCons ckey cvalue tl => if ckey = key then Return (ListCons ckey value tl) else do tl0 <- hash_map_insert_in_list_loop_back key value tl; Return (ListCons ckey cvalue tl0) od | ListNil => (let l = ListNil in Return (ListCons key value l)) [hash_map_insert_in_list_loop_fwd_def] Definition ⊢ ∀key value ls. hash_map_insert_in_list_loop_fwd key value ls = case ls of ListCons ckey cvalue tl => if ckey = key then Return F else hash_map_insert_in_list_loop_fwd key value tl | ListNil => Return T [hash_map_insert_no_resize_fwd_back_def] Definition ⊢ ∀self key value. hash_map_insert_no_resize_fwd_back self key value = do hash <- hash_key_fwd key; i <<- vec_len self.hash_map_slots; hash_mod <- usize_rem hash i; l <- vec_index_mut_fwd self.hash_map_slots hash_mod; inserted <- hash_map_insert_in_list_fwd key value l; if inserted then do i0 <- usize_add self.hash_map_num_entries (int_to_usize 1); l0 <- hash_map_insert_in_list_back key value l; v <- vec_index_mut_back self.hash_map_slots hash_mod l0; Return (self with <|hash_map_num_entries := i0; hash_map_slots := v|>) od else do l0 <- hash_map_insert_in_list_back key value l; v <- vec_index_mut_back self.hash_map_slots hash_mod l0; Return (self with hash_map_slots := v) od od [hash_map_len_fwd_def] Definition ⊢ ∀self. hash_map_len_fwd self = Return self.hash_map_num_entries [hash_map_move_elements_from_list_fwd_back_def] Definition ⊢ ∀ntable ls. hash_map_move_elements_from_list_fwd_back ntable ls = hash_map_move_elements_from_list_loop_fwd_back ntable ls [hash_map_move_elements_from_list_loop_fwd_back_def] Definition ⊢ ∀ntable ls. hash_map_move_elements_from_list_loop_fwd_back ntable ls = case ls of ListCons k v tl => do ntable0 <- hash_map_insert_no_resize_fwd_back ntable k v; hash_map_move_elements_from_list_loop_fwd_back ntable0 tl od | ListNil => Return ntable [hash_map_move_elements_fwd_back_def] Definition ⊢ ∀ntable slots i. hash_map_move_elements_fwd_back ntable slots i = hash_map_move_elements_loop_fwd_back ntable slots i [hash_map_move_elements_loop_fwd_back_def] Definition ⊢ ∀ntable slots i. hash_map_move_elements_loop_fwd_back ntable slots i = (let i0 = vec_len slots in if usize_lt i i0 then do l <- vec_index_mut_fwd slots i; ls <<- mem_replace_fwd l ListNil; ntable0 <- hash_map_move_elements_from_list_fwd_back ntable ls; i1 <- usize_add i (int_to_usize 1); l0 <<- mem_replace_back l ListNil; slots0 <- vec_index_mut_back slots i l0; hash_map_move_elements_loop_fwd_back ntable0 slots0 i1 od else Return (ntable,slots)) [hash_map_new_fwd_def] Definition ⊢ hash_map_new_fwd = hash_map_new_with_capacity_fwd (int_to_usize 32) (int_to_usize 4) (int_to_usize 5) [hash_map_new_with_capacity_fwd_def] Definition ⊢ ∀capacity max_load_dividend max_load_divisor. hash_map_new_with_capacity_fwd capacity max_load_dividend max_load_divisor = (let v = vec_new in do slots <- hash_map_allocate_slots_fwd v capacity; i <- usize_mul capacity max_load_dividend; i0 <- usize_div i max_load_divisor; Return <|hash_map_num_entries := int_to_usize 0; hash_map_max_load_factor := (max_load_dividend,max_load_divisor); hash_map_max_load := i0; hash_map_slots := slots|> od) [hash_map_remove_back_def] Definition ⊢ ∀self key. hash_map_remove_back self key = do hash <- hash_key_fwd key; i <<- vec_len self.hash_map_slots; hash_mod <- usize_rem hash i; l <- vec_index_mut_fwd self.hash_map_slots hash_mod; x <- hash_map_remove_from_list_fwd key l; case x of NONE => do l0 <- hash_map_remove_from_list_back key l; v <- vec_index_mut_back self.hash_map_slots hash_mod l0; Return (self with hash_map_slots := v) od | SOME x0 => do i0 <- usize_sub self.hash_map_num_entries (int_to_usize 1); l0 <- hash_map_remove_from_list_back key l; v <- vec_index_mut_back self.hash_map_slots hash_mod l0; Return (self with <|hash_map_num_entries := i0; hash_map_slots := v|>) od od [hash_map_remove_from_list_back_def] Definition ⊢ ∀key ls. hash_map_remove_from_list_back key ls = hash_map_remove_from_list_loop_back key ls [hash_map_remove_from_list_fwd_def] Definition ⊢ ∀key ls. hash_map_remove_from_list_fwd key ls = hash_map_remove_from_list_loop_fwd key ls [hash_map_remove_from_list_loop_back_def] Definition ⊢ ∀key ls. hash_map_remove_from_list_loop_back key ls = case ls of ListCons ckey t tl => if ckey = key then (let mv_ls = mem_replace_fwd (ListCons ckey t tl) ListNil in case mv_ls of ListCons i cvalue tl0 => Return tl0 | ListNil => Fail Failure) else do tl0 <- hash_map_remove_from_list_loop_back key tl; Return (ListCons ckey t tl0) od | ListNil => Return ListNil [hash_map_remove_from_list_loop_fwd_def] Definition ⊢ ∀key ls. hash_map_remove_from_list_loop_fwd key ls = case ls of ListCons ckey t tl => if ckey = key then (let mv_ls = mem_replace_fwd (ListCons ckey t tl) ListNil in case mv_ls of ListCons i cvalue tl0 => Return (SOME cvalue) | ListNil => Fail Failure) else hash_map_remove_from_list_loop_fwd key tl | ListNil => Return NONE [hash_map_remove_fwd_def] Definition ⊢ ∀self key. hash_map_remove_fwd self key = do hash <- hash_key_fwd key; i <<- vec_len self.hash_map_slots; hash_mod <- usize_rem hash i; l <- vec_index_mut_fwd self.hash_map_slots hash_mod; x <- hash_map_remove_from_list_fwd key l; case x of NONE => Return NONE | SOME x0 => monad_ignore_bind (usize_sub self.hash_map_num_entries (int_to_usize 1)) (Return (SOME x0)) od [hash_map_try_resize_fwd_back_def] Definition ⊢ ∀self. hash_map_try_resize_fwd_back self = do max_usize <- mk_usize (u32_to_int core_num_u32_max_c); capacity <<- vec_len self.hash_map_slots; n1 <- usize_div max_usize (int_to_usize 2); (i,i0) <<- self.hash_map_max_load_factor; i1 <- usize_div n1 i; if usize_le capacity i1 then do i2 <- usize_mul capacity (int_to_usize 2); ntable <- hash_map_new_with_capacity_fwd i2 i i0; (ntable0,_) <- hash_map_move_elements_fwd_back ntable self.hash_map_slots (int_to_usize 0); Return (ntable0 with <|hash_map_num_entries := self.hash_map_num_entries; hash_map_max_load_factor := (i,i0)|>) od else Return (self with hash_map_max_load_factor := (i,i0)) od [test1_fwd_def] Definition ⊢ test1_fwd = do hm <- hash_map_new_fwd; hm0 <- hash_map_insert_fwd_back hm (int_to_usize 0) (int_to_u64 42); hm1 <- hash_map_insert_fwd_back hm0 (int_to_usize 128) (int_to_u64 18); hm2 <- hash_map_insert_fwd_back hm1 (int_to_usize 1024) (int_to_u64 138); hm3 <- hash_map_insert_fwd_back hm2 (int_to_usize 1056) (int_to_u64 256); i <- hash_map_get_fwd hm3 (int_to_usize 128); if i ≠ int_to_u64 18 then Fail Failure else do hm4 <- hash_map_get_mut_back hm3 (int_to_usize 1024) (int_to_u64 56); i0 <- hash_map_get_fwd hm4 (int_to_usize 1024); if i0 ≠ int_to_u64 56 then Fail Failure else do x <- hash_map_remove_fwd hm4 (int_to_usize 1024); case x of NONE => Fail Failure | SOME x0 => if x0 ≠ int_to_u64 56 then Fail Failure else do hm5 <- hash_map_remove_back hm4 (int_to_usize 1024); i1 <- hash_map_get_fwd hm5 (int_to_usize 0); if i1 ≠ int_to_u64 42 then Fail Failure else do i2 <- hash_map_get_fwd hm5 (int_to_usize 128); if i2 ≠ int_to_u64 18 then Fail Failure else do i3 <- hash_map_get_fwd hm5 (int_to_usize 1056); if i3 ≠ int_to_u64 256 then Fail Failure else Return () od od od od od od *) end